Jakob Björnberg

The interchange model and related spin systems on two-block graphs

The interchange model is a model in quantum statistical physics with close connections to random permutations. In joint (almost completed) work with Hjalmar Rosengren and Kieran Ryan we recently analysed such models in a "two-block" setting. This includes complete bipartite graphs as a special case. Our method exploits algebraic aspects of the model and allows us to obtain explicit expressions for certain limiting quantities. In the "probabilistic regime" (which includes the Heisenberg ferromagnet) our results may be interpreted in terms of the appearance of macroscopic permutation cycles. In other regimes we obtain an intriguing phase diagram.